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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#352119#7730. Convex Checker_SheepsheepWA 51ms19348kbC++177.5kb2024-03-12 21:16:232024-03-12 21:16:24

Judging History

你现在查看的是最新测评结果

  • [2024-07-04 19:27:17]
  • hack成功,自动添加数据
  • (/hack/727)
  • [2024-07-04 19:17:30]
  • hack成功,自动添加数据
  • (/hack/726)
  • [2024-03-12 21:16:24]
  • 评测
  • 测评结果:WA
  • 用时:51ms
  • 内存:19348kb
  • [2024-03-12 21:16:23]
  • 提交

answer

#include<bits/stdc++.h>
using namespace std ;
#define ll long long
const int inf = 1e8 ;
const int N = 3e6+9 ;
typedef long double LD ;
const LD eps = 1e-7 ;
const LD box = 1e7 ;
int sgn( LD x )
{
    return x > eps ? 1 : ( x < -eps ? -1 : 0 ) ;
}
struct point
{
    LD x , y , polar_angle;
    point operator + (const point &a) const
    {
        return{ x+a.x , y+a.y } ;
    }
    point operator - (const point &a) const
    {
        return{ x-a.x , y-a.y } ;
    }
    point operator * (const LD &a) const
    {
        return{ x*a , y*a } ;
    }
    point operator / (const LD &a) const
    {
        return{ x/a , y/a } ;
    }
    friend bool operator == ( const point &a , const point &b )
    {
        return sgn(a.x-b.x) == 0 && sgn(a.y-b.y) == 0 ;
    }

    friend ostream & operator << ( ostream &out , point &a )
    {
        out << "(" << a.x << "," << a.y << ")" ;
        return out ;
    }
    friend istream & operator >> ( istream &in , point &a )
    {
        in >> a.x >> a.y ;
        return in ;
    }
    int idx , hull_rank ;
};
struct line
{
    point s , t ;
    friend bool operator == ( const line &a , const line &b )
    {
        return (a.s==b.s&&a.t==b.t)||(a.s==b.t&&a.t==b.s) ;
    }
};
LD sqr( LD x )
{
    return x*x ;
}
LD mo( point x )
{
    return sqrtl( sqr(x.x) + sqr(x.y) ) ;
}
LD dis( const point &a , const point &b )
{
    return sqrtl( sqr(a.x-b.x) + sqr(a.y-b.y) ) ;
}
LD dot( const point &a , const point &b )
{
    return a.x*b.x+a.y*b.y;
}
LD det( const point &a , const point &b )
{
    // + : b ? a ??????
    return a.x*b.y-b.x*a.y ;
}
bool point_on_segment( const point &a , const line &l )
{
    if( l.s == l.t )
    {
        return a == l.s ;
    }
    return sgn( det(l.s-a,a-l.t) ) == 0 && sgn( dot(l.s-a,l.t-a) ) <= 0 ;
}
bool two_side( const point &a , const point &b , const line &c )
{
    // ???????
    return sgn( det(a-c.s,c.t-c.s) ) * sgn( det(b-c.s,c.t-c.s) ) < 0 ;
}
bool segment_inter_judge( const line &a , const line &b )
{
    bool ok = 0 ;
    ok |= point_on_segment( b.s , a ) ;
    ok |= point_on_segment( b.t , a ) ;
    ok |= point_on_segment( a.s , b ) ;
    ok |= point_on_segment( a.t , b ) ;
    ok |= ( two_side(a.s,a.t,b)&&two_side(b.s,b.t,a) ) ;
    return ok ;
}
bool ray_inter_judge( const line &a , const line &b )
{
    //??????????
    return sgn( det( a.t-a.s , b.t-b.s ) ) == 0 ? 0 : 1 ;
}
LD point_to_line( const point &p , const line &l )
{
    return fabs( det(l.t-l.s,p-l.s) )/dis(l.s,l.t) ;
}
LD point_to_segment( const point &p , const line &l )
{
    if( l.s == l.t ) return dis( p , l.s ) ;
    if( sgn( dot(l.s-p,l.t-l.s) )*sgn( dot(l.t-p,l.t-l.s) ) <= 0 ) return point_to_line(p,l) ;
    else return min( dis(p,l.s) , dis(p,l.t) ) ;
}
LD arg( const line &a , const line &b )
{
    LD res = dot( a.t-a.s , b.t-b.s ) ;
    res /= mo( a.t-a.s ) ;
    res /= mo( b.t-b.s ) ;
    return acos( res ) ;
}
point line_intersect( const line &a , const line &b )
{
    LD u = det( a.t-a.s,b.s-a.s ) ;
    LD v = det( a.t-a.s , b.t-a.s ) ;
    return ( b.s*v - b.t*u )/(v-u) ;
}
bool turn_left( const point &a , const point &b , const point &c )
{
    // a ???????ac????ab??????????
    return sgn( det( b-a , c-a ) ) > 0 ;
}
bool turn_right( const point &a , const point &b , const point &c )
{
    return sgn( det( b-a , c-a ) ) < 0 ;
}
bool turn_left( const line &a , const line &b , const line &c )
{
    // bc?????????a???
    return turn_left( a.s , a.t , line_intersect(b,c) ) ;
}
int point_quadrant( const point &a )
{
    if( sgn( a.x ) >= 0 && sgn( a.y ) >= 0 ) return 1 ;
    else if( sgn(a.x) < 0 && sgn( a.y ) >= 0 ) return 2 ;
    else if( sgn(a.x) < 0 && sgn( a.y ) < 0 ) return 3 ;
    else return 4 ;

}
vector<point> convex_hull( vector<point> a )
{
    vector<point>ret ;
    int a_size = a.size() , ret_size = 0 ;
    if( a_size <= 2 ) return a ;
    sort( a.begin() , a.end() , []( point x , point y ){ return x.x == y.x ? x.y < y.y : x.x < y.x ; } )  ;
    for( int i = 0 ; i < a_size ; i ++ )
    {
        while( ret_size > 1 && !turn_left( ret[ret_size-2] , ret[ret_size-1] , a[i] ) )
        {
            ret.pop_back() ; ret_size -- ;
        }
        ret.push_back( a[i] ) ; ret_size ++ ;
    }
    int fix = ret_size ;
    for( int i = a_size-2 ; i >= 0 ; i -- )
    {
        while( ret_size > fix && !turn_left( ret[ret_size-2] , ret[ret_size-1] , a[i] ) )
        {
            ret.pop_back() ; ret_size -- ;
        }
        ret.push_back( a[i] ) ; ret_size ++ ;
    }
    ret.pop_back() ; ret_size -- ;

    return ret ;
}
int half( const point &a ) //???????
{
    return a.y > 0 || ( a.y == 0 && a.x > 0 ? 1 : 0 );
}
bool is_para( const line &a , const line &b ) //?????
{
    return sgn( det(a.t-a.s,b.t-b.s) ) == 0 ;
}
bool cmp( const line &a , const line &b )
{
    // (0,0) is org
    int sign = half( a.t-a.s ) - half( b.t-b.s ) ; //????????
    int dir = sgn( det(a.t-a.s,b.t-b.s) ) ; //????

    if( sign == 0 && dir == 0 ) return sgn( det(a.t-a.s , b.t-a.s) ) < 0 ; //??????
    else return sign ? sign > 0 : dir > 0 ;
    //???????????
    //??????????
}
vector<point> hpi( vector<line> A , LD DX , LD DY )
{
    int siz_a = A.size() ;
    vector<line>h ;
    for( int i = 0 ; i < siz_a ; i ++ ) h.push_back( A[i] ) ;

    h.push_back( {{DX,DY} , {0,DY}} ) ;
    h.push_back( {{0,DY} , {0,0}} ) ;
    h.push_back( {{0,0} , {DX,0}} ) ;
    h.push_back( {{DX,0} , {DX,DY}} ) ;
    sort( h.begin() , h.end() , cmp ) ;

    vector<line> q( h.size()+10 ) ;
    int l = 0 , r = -1 ;
    for( auto &i : h )
    {
        while( l<r && !turn_left(i,q[r-1],q[r]) ) --r ;
        while( l<r && !turn_left(i,q[l],q[l+1]) ) ++l ;
        if( l <= r && is_para(i,q[r]) ) continue ;
        q[++r] = i ;
    }
    while( r-l>1 && !turn_left(q[l],q[r-1],q[r]) ) --r ;
    while( r-l>1 && !turn_left(q[r],q[l],q[l+1]) ) ++l ;

    if( r-l < 2 ) return {} ;
    vector<point> ret(r-l+1) ;
    for( int i = l ; i <= r ; i ++ )
        ret[i-l] = line_intersect( q[i] , q[i==r?l:i+1] ) ;
    return ret ;
}
bool on_box( point a )
{
    if( sgn(a.x-box) == 0 || sgn(a.y-box) == 0 ) return 1 ;
    return 0;
}
bool is_open( vector<point>ret )
{
    if( ret.size() <= 2 )
    for( auto &u : ret ) if( on_box(u) ) return 1 ;
    return 0 ;
}
void solve()
{
    int n ; cin >> n ;
    vector<point>a(n),b(n);
    for( int i = 0 ; i < n ; i ++ )
    {
        cin >> a[i] ; b[i] = a[i] ;
        if( i > 0 ) b[i].polar_angle = atan2( b[i].y-b[0].y , b[i].x-b[0].x ) ;
    }

    bool ok1 = 1 , ok2 = 1 ;
    sort( b.begin()+1 , b.end() , [&]( point x , point y ){ return x.polar_angle < y.polar_angle; } ) ;
    for( int i = 0 ; i < n ; i ++ ) if( !(a[i] == b[i]) ) ok1 = 0 ;

    sort( b.begin()+1 , b.end() , [&]( point x , point y ){ return x.polar_angle > y.polar_angle; } ) ;
    for( int i = 0 ; i < n ; i ++ ) if( !(a[i] == b[i]) ) ok2 = 0 ;

    if( !ok1 && ! ok2 )
    {
        cout << "No\n" ; return ;
    }
    if( !turn_left( a[0] , a[1] , a[2] ) && !turn_right( a[0] , a[1] , a[2] ) )
    {
        cout << "No\n" ; return ;
    }

    bool ok = 1 ;

    if( turn_left( a[0] , a[1] , a[2] ) )
    {
        for( int i = 2 ; i < n ; i ++ )
        {
            if( !turn_left( a[i-1] , a[i] , a[(i+1)%n] ) ) ok = 0 ;
        }
    }
    else
    {
        for( int i = 2 ; i < n ; i ++ )
        {
            if( !turn_right( a[i-1] , a[i] , a[(i+1)%n] ) ) ok = 0 ;
        }
    }

    if( ok ) cout << "Yes\n" ;
    else cout << "No\n" ;

}
int main()
{
    ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
    int tt = 1 ; //cin >> tt ;
    while( tt-- ) solve() ;
    return 0 ;
}
/*
5 4.321
-2 -1 3 -2
1 6 3 -2
1 6 -2 -1
-3 4 3 3
-2 1 5 4
*/

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 0ms
memory: 3784kb

input:

3
0 0
1 0
0 1

output:

Yes

result:

ok answer is YES

Test #2:

score: 0
Accepted
time: 0ms
memory: 3816kb

input:

4
0 0
0 1
1 1
1 0

output:

Yes

result:

ok answer is YES

Test #3:

score: 0
Accepted
time: 0ms
memory: 3932kb

input:

4
0 0
0 3
1 2
1 1

output:

Yes

result:

ok answer is YES

Test #4:

score: 0
Accepted
time: 0ms
memory: 3788kb

input:

3
0 0
0 0
0 0

output:

No

result:

ok answer is NO

Test #5:

score: 0
Accepted
time: 0ms
memory: 3776kb

input:

5
1 0
4 1
0 1
2 0
3 2

output:

No

result:

ok answer is NO

Test #6:

score: 0
Accepted
time: 0ms
memory: 3936kb

input:

5
0 0
1000000000 0
1000000000 500000000
1000000000 1000000000
0 1000000000

output:

No

result:

ok answer is NO

Test #7:

score: 0
Accepted
time: 1ms
memory: 3772kb

input:

5
0 0
1000000000 0
1000000000 499999999
1000000000 1000000000
0 1000000000

output:

No

result:

ok answer is NO

Test #8:

score: 0
Accepted
time: 0ms
memory: 3776kb

input:

5
0 0
999999999 0
1000000000 50000000
999999999 1000000000
0 1000000000

output:

Yes

result:

ok answer is YES

Test #9:

score: 0
Accepted
time: 51ms
memory: 19348kb

input:

128312
5578014 410408218
5585076 410404717
5588011 410403262
5588473 410403033
5589740 410402405
5593295 410400643
5593751 410400417
5597248 410398684
5598935 410397848
5600618 410397014
5605185 410394751
5610514 410392111
5614281 410390245
5617263 410388768
5621142 410386847
5630840 410382045
56310...

output:

Yes

result:

ok answer is YES

Test #10:

score: -100
Wrong Answer
time: 50ms
memory: 19016kb

input:

128086
149550602 509469827
149551059 509465022
149551336 509462107
149551964 509455497
149552572 509449094
149553350 509440895
149553656 509437667
149554161 509432339
149554254 509431357
149554545 509428284
149555017 509423299
149555366 509419611
149555842 509414580
149556382 509408867
149556564 509...

output:

No

result:

wrong answer expected YES, found NO